New Infinite Families of $3$-Designs from Algebraic Curves of Higher Genus over Finite Fields

New Infinite Families of 3-Designs from Algebraic Curves of Higher Genus over Finite Fields

In this paper, we give a simple method for computing the stabilizer subgroup of D(f) = {α ∈ Fq | there is a β ∈ Fq such that βn = f(α)} in PSL2(Fq), where q is a large odd prime power, n is a positive integer dividing q − 1 greater than 1, and f(x) ∈ Fq[x]. As an application, we construct new infinite families of 3-designs.

Curves of Genus 3 over Small Finite Fields

Curves of Genus 3 over Small Finite Fields

Curves of Genus 3 over Small Finite Fields

The maximal number of rational points that a (smooth, geometrically irreducible) curve of genus g over a finite field lF, of cardinality q can have, is denoted by Nq(g). The interest in this number, particularly for fixed q as a function of g, arose primarily during the last two decades from applications to error correcting codes [Lath], [T-G-Z], [vL-vdG]. A lot of results on N,(g) for fixed q ...

Workshop on Algebraic Curves Over Finite Fields

Let L(t) = 1+a1t+ · · ·+a2gt be the numerator of the zeta function of an algebraic curve C defined over the finite field Fq of genus g. We show that the coefficients ar of L(t) satisfy certain inequalities. Conversely, for any integers a1, . . . , am satisfying these inequalities and all sufficiently large integers g there exist curves of genus g, whose L-polynomial satisfies the following cong...